An Equivalent Form of the Prime Number Theorem
DOI:
https://doi.org/10.5644/SJM.15.02.08Keywords:
Dirichlet series, Prime Number TheoremAbstract
A simple proof is given that $\sum\limits_{n}\frac{\mu(n) d(n)}{n}=0$ using the Prime Number Theorem. It is shown that this is equivalent to the estimate $\sum\limits_{n\leq x}\mu(n)d(n)=\circ(x)$ and to the Prime Number Theorem.
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